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2. Level Circuit LS Adjustment

For the leveling circuit in Figure B-1

Figure B-1
Level Circuit

and these observed elevation differences

Obs Line dElev   Obs Line dElev
1 BMA-Q +8.91   5 BMA-R -3.56
2 BMB-Q -2.92     -- --
3 BMC-Q -4.67   6 BMC-R -17.12
4 BMD-Q -8.66   7 BMD-R -21.10

what are the elevations of points Q and R?

A traditional simple adjustment is difficult to apply in this situation. Because point Q is connected to four benchmarks and point R to three, any simple adjustment attempted will result in multiple elevations for each point.

With a small network like this, a Brute Force approach might be feasible. Using the observed elevation differences, compute all possible elevations for points Q and R, then simply average them.

Point Q elevations and their average are:

Similarly, for point R:

Compute So

Compute residuals using the adjusted elevations and the individually computed elevations used for the averages.
v = MPVQ-ElevQ v2 sums 
-0.015 0.000225  
+0.015 0.000225  
-0.035 0.001225  
+0.035 0.001225 0.002900 
v = MPVR-ElevR v2  
+0.007 0.000049  
-0.033 0.001089  
+0.027 0.000729 0.001867 
There are seven observations (m) and two unknown elevations (n).

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